Having some interesting questions in my favorite list that could help me if I stumble over them in the future, I wondered about how long the questions and answers will be stored (so, if I should save some of my favorites offline to still have access to them in a year). Of course there can't be a guarantee that SO will still be available, but if it is, will my favorite question also be? Or is there some sort of "timeout" and questions/answers get deleted from the database after some time?

One issue is that "correct answers" for many problems may no longer be the best answer down the line. Even if someone posts a new, updated, even more correct answer on a post later on (unlikely, there's 60k questions now, so old questions will be found by people looking for answers, not looking to give answers) it is unlikely that they will be scored up, or accepted.

So the site needs to ensure that old questions are "rebubbled" to the top occasionally - in a year or two at least, to get updated answers and keep them alive, maybe get some more upvotes for still correct answers.

I wouldn't worry too much about the data being lost any time soon. It has been created for developers by developers, and even if, at some point in the future, they decide to shut the whole thing down, I couldn't imagine that anyone (especially our lovable overlords J & J) wouldn't at least offer the database to someone else to host: even as a static archive.